Note that x^2 is in the denominator. The way you had it is NOT a bessel equation. So now that we have this, what do we do?
Well, we know that the solutions to the following equation
So let's compare this to your equation.
These are our equations
We find the solutions to be
Therefore, the part of the general solution that they want is
Of course K is a constant so we can let a new constant A absorb that value.